Fault Diagnosis of Chemical Processes Using Artificial Immune

Article pubs.acs.org/IECR

Fault Diagnosis of Chemical Processes Using Artificial Immune System with Vaccine Transplant Yidan Shu and Jinsong Zhao* State Key Laboratory of Chemical Engineering, Department of Chemical Engineering, Tsinghua University, Beijing, China ABSTRACT: Chemical process accidents have tremendous impacts on the environment, as well as the sustainability of the chemical industry. Fault detection and diagnosis (FDD) are important to ensure safety and stability of chemical processes. However, the scarcity of fault samples has limited the wide application of FDD methods in the industry. In this work, we present an artificial immune system (AIS)-based FDD approach for diagnosing faults in the chemical processes without historical fault samples. This approach mimics the vaccine transplant in the medicine discipline. Historical fault samples collected from other chemical processes of the same type are used to generate vaccines to help construct fault antibody libraries for the diagnosis objective process. Case studies on the Pensim process and laboratory-scale distillation columns illustrate the effectiveness of our approach.

1. INTRODUCTION Sustainable manufacturing refers to the production of goods using processes and materials designed to minimize the product’s environmental footprint, according to the definition presented by the Science and Technology Policy Institute (STPI) in its “White Papers on Advanced Manufacturing Questions”.1Much attention has been paid to the reduction of energy cost and material waste in the normal state of processes. However, chemical process accidents have also tremendous impacts on the environment, although their occurrence frequency is low. Because chemical processes often involve flammable, explosive, or toxic materials and extreme operating conditions such as high temperature or high pressure, faults in chemical processes may lead to disastrous scenarios and cause tremendous losses of health, environment, and economics and impact the sustainability of manufacturing. For example, the explosion accident of the BP deepwater horizon platform in 2010 discharged 780 million liters (4.9 million barrels) of crude oil into the Gulf of Mexico;2 the explosion accident of the Jilin chemical plant in 2005 polluted the Songhua River in China with ∼100 tons of pollutants containing benzene and nitrobenzene.3 Fault detection and diagnosis (FDD), which has been studied over the past half century, is one of the important technologies of sustainable manufacturing, since it can provide timely decision support for the operators to take actions to prevent the chemical processes from deviating from the safe operation range. Fault detection and diagnosis methodologies can be classified into three classes, namely, (i) qualitative model-based methods, (ii) quantitative model-based methods, and (iii) process-historybased methods.4−6 As modern chemical processes become larger and more complex, process-history-based methods show advantages over the other two classes of methods, because of its independency of prior knowledge and models about the processes. Many process-history-based methods have been proposed, such as principal component analysis (PCA),7−9 independent component analysis (ICA),10,11artificial neural networks (ANN),12,13 dynamic locus analysis (DLA),14 Petri nets,15,16 and so on. Among them, the artificial immune system (AIS) has its own advantages of strong adaptive and self− © XXXX American Chemical Society

learning ability to diagnose new fault types and the low requirement for the number of historical samples for training.17−21 Dai and Zhao integrated AIS with dynamic time warping (DTW) for batch process fault diagnosis22 and afterward used the so-called “dynamic artificial immune system” (DAIS) in an online fault diagnosis strategy for full operating cycles of chemical processes.23 However, the above fault diagnosis methods all rely upon fault samples of the chemical process to be diagnosed. In fact, since faults do not often occur, there may be no historical fault samples in a chemical process at all, especially in a newly established one. Therefore, few successful industrial applications of process fault diagnosis technologies have been reported, because of the barrier of fault samples. It is well-known in the chemical industry that processes are more vulnerable to abnormal situations during the startup of a new chemical process.24 However, rapid changes in chemical products and global competition pushed researchers and engineers of chemical plants to develop new chemical processes.25 Therefore, there exists an urgent need to break down the fault sample barrier to pave the way for real industrial applications of fault diagnosis technologies. Even though the DAIS developed by the authors requires fewer fault samples, it cannot work without any fault sample available. Facco et al. proposed the joint-Y PLS method to transfer process monitoring models between plants and applied the method in both continuous and batch processes.26−28The Joint-Y PLS could monitor the state of a process with few historical normal samples. However, the method proposed by Facco was designed for fault detection and could not diagnose the type of faults that were occurring. In this paper, we present an approach to improve the applicability of DAIS in cases where the historical fault samples Special Issue: Sustainable Manufacturing Received: July 20, 2015 Revised: October 25, 2015 Accepted: November 19, 2015

A

DOI: 10.1021/acs.iecr.5b02646 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research

mathematical and computational modeling of immunology, abstraction from those models into algorithm (and system) design and implementation in the context of engineering. In 1990, AIS was used by Ishida30 for fault diagnosis of sensor networks. Since then, AIS has been widely used in diverse fields of engineering application. Most of this research can be found in reviews of AIS.18,31,32Recent work on process system fault diagnosis has also been reported. Aguilar19 proposed a pattern recognition model based on AIS to conduct fault detection. Wang and Zhao20studied the application of AIS in fault diagnosis of the Tennessee Eastman (TE) process. Ghosh and Srinivasan21 also proposed an immune-system-inspired approach for process monitoring and fault diagnosis and illustrated its effectiveness in several case studies. Their approach was based on the negative selection algorithm. To apply AIS in fault diagnosis of batch processes, Dai and Zhao integrated the clonal selection algorithm of AIS with DTW22and afterward used the DAIS in an online fault diagnosis strategy for full operating cycles of chemical processes.23 Our method of vaccine transplant is mainly based on the DAIS proposed in refs 22 and 23, with some modifications. Learning from the concepts in adaptive immunity, DAIS generates antibodies from historical data, clones them with mutation to construct the antibody libraries, and compared the antibodies in libraries with the antigens generated from the online data in order to recognize the online conditions. The details of DAIS used in our proposed method will be discussed in the remaining of this section, including the difference calculation, the generation of antibodies and antigens from process data, and the construction of antibody libraries. The vaccine transplant then will be discussed in the next section. 2.3. Difference Calculation Based on Dynamic Time Warping (DTW). One of the key issues in DAIS is the calculation of the degree of difference between antigens and antibodies, which is similar to the affinity between antigens and antibodies in HIS. The Euclidean distance is not suitable for determining the difference between two matrices containing trend information, because the two trends may not perfectly align. DTW is a flexible method for comparing two dynamic patterns that may not be perfectly aligned and are characterized by similar, but possibly expanded or contracted, temporal correlations.33 DTW was first used in the area of speech recognition. Kassidas et al. first utilized it for fault detection and diagnosis of chemical process.34 The main idea of DTW is to find a minimum sequence F of K-points on an l × m grid:

are unavailable. The approach is based on the idea that historical samples generated from other chemical processes of the same type can be used to build antibody libraries of AIS. This idea comes from the use of vaccines that helps the human immune system build antibodies with weakened pathogens from somewhere else, so the approach is called vaccine transplant. During the clone and mutation processes of AIS, antibodies of faults that have never occurred in one process can be built from historical samples of the same type of faults from other chemical processes of the same type. This approach allows sharing of fault knowledge among chemical processes, thus making it possible to overcome the fault sample barrier that has been existing for decades in the discipline of fault diagnosis. The remaining parts of this paper are organized as below: Section 2 will briefly introduce DAIS; then Section 3 will present the framework of our antibody transplant approach; Sections 4 and 5are case studies on the Pensim simulated process and a laboratory-scale distillation column to illustrate the effectiveness of our approach; Section 6 is the conclusion.

2. DYNAMIC ARTIFICIAL IMMUNE SYSTEM 2.1. Human Immune System (HIS). The human immune system (HIS) is a defense system that protects human bodies from pathogens (harmful micro-organisms such as bacteria and viruses).29 It is comprised of the organs, cells, and chemical components of the body that provide resistance to infection and toxins. There are two types of immunity: innate immunity and adaptive immunity. Innate immunity is the natural resistance with which a person is born. It is present before the onset of infection and contributes a set of disease-resistance mechanism that is not specific to particular pathogens. Innate immunity provides the first defense line against infections. Adaptive immunity is the immunity that is acquired through contact with the disease-causing agents. When the body is attacked by the pathogens, adaptive immunity will respond to the pathogens with a high degree of specificity. Such a degree of specificity comes from the specific binding between the antigens and antibodies. Antigen is a special substance that comes from the pathogens that may provoke immunity response, while antibody is a Y-shaped protein generated by the adaptive immunity to specially bind with a type of antigen. The special binding between the antigens and antibodies will help the immune system to recognize and clear the pathogens. The adaptive immunity may also have the remarkable property of “memory”, which means that the immunity may keep the memories of a certain type of antibodies and will have a quicker and stronger response to future attacks from the same pathogens. Similar to the innate immunity, in chemical processes, control systems are deployed to protect the processes from disturbances. However, if a disturbance causes a departure that is not within the acceptable range of an observed variable or a specific state parameter in a chemical process, a fault might occur. Fault diagnosis then is necessary to recognize what type of fault occurs and help the operators to take correct actions to bring the chemical process back to the safe operation range. The principle of adaptive immunity can be used for fault diagnosis in chemical processes. 2.2. Artificial Immune System. As summarized by Timmis,17 AIS is a diverse area of research that attempts to bridge the gap between immunology and engineering and it is developed through the application of techniques such as

F = {c(1), c(2), ..., c(k), ..., c(K )}

(1)

c(k) = [i(k), j(k)]

(2)

Let Ab and Ag respectively denote antibody and antigen, with respective dimensions of m × n and l × n, where n is the number of variables and r and t represent the lengths of the data for the variables in each matrix, respectively. In DTW, first an l × m matrix (d), representing the Euclidean distance between R and T, is calculated: n

d ( i , j) =

∑ (ωc|Ab(j , c) − Ag(i , c)|) c=1

(3)

where i and j denote the sample times in T and R, respectively, c denotes the variables of R and T, and ωc denotes the non-negative B


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Industrial & Engineering Chemistry Research weight of variable c. In our proposed approach, ωc is 1 for all variables. Using the Itakura constraint,31 another matrix (D), representing the dissimilarity distance between Ab and Ag is then formulated:

sampling point of fault introduction moment in the fault sample, and m is the length of antibodies, which is taken to be 60 in this work. The information on deviation trends presented by the original antibodies may also be mixed with the differences of the operating conditions of the normal samples and the fault samples. To eliminate the effects of such differences, a modification item is added into eq 10, as shown in eq 11:

⎧ D(i − 1, j) + d(i , j) or [∞ , if condition (A)]⎫ ⎪ ⎪ ⎪ ⎪ ⎬ D(i , j) = min⎨ D(i − 1, j − 1) + d(i , j) ⎪ ⎪ ⎪ D(i − 1, j − 2) + d(i , j) ⎪ ⎩ ⎭ (4)

×n AbmF,modified = [HF(1) − HN(k) − Ms1 × n ; ...;

HF(m) − HN(k + m − 1) − Ms1 × n]

where D(1, j) = d(1, j) and condition (A) indicates that the predecessor of point (i − 1, j) is the point (i − 2, j). Hence, the point j* in the last column of the matrix D corresponding to the minimum distance between Ab and Ag can be determined: j* = arg minj{D(l , j)}

j ∈ [1, m]

where M1×n is a 1 × n modification item obtained by averaging s the difference of s sampling points before the fault introduction moment between HF and HN: Ms1 × n =

(5)

The sequence F* that matches Ab to Ag is described as F * = {(1, j(1)), (2, j(2)), ..., (l , j(l))}

(6)

∑ |Ab(j(i), c) − Ag(i , c)|

x − X min X max − X min

(13)

(14)

×n Ag ldetective = [Ag1, Ag 2 , ..., Ag n] = T

(15)

After a fault is detected, a diagnostic antigen is generated with the l samples before the fault detection moment: ×n Ag ldiagnostic = [T (1) − HN(k); T(2) − HN(k + 1); ...;

T (l) − HN(k + l − 1)]

(16)

where k is the sequence number of a sampling point of the normal historical sample that associate with the fault detection moment, according to the sequence matching the historical normal sample and online sample, according to eqs 1−6. Considering the differences of the process statuses between the online process data and the historical normal samples, the antigen calculation should be modified with an extra item, as eq 17 shows:

(9)

where x is the actual data, Xmax the maximum value of historical normal samples, Xmin the minimum value of historical normal samples, and X the normalized data. The original fault antibody is composed of the deviation matrix between the historical fault samples (HF) after the fault was introduced and the historical normal samples (HN):

×n Ag ldiagnostic,modified

= [T (1) − HN(k) − Ms1 × n ; ...; T (l) − HN(k + l − 1) − Ms1 × n] (17)

AbmF × n = [HF(1) − HN(k); HF(2) − HN(k + 1); ...; HF(m) − HN(k + m − 1)]

(12)

where T(i) is the value of variables after a fault is introduced, n the number of variables, and l the selected length of antigens. During fault detection, the detective antigen is composed of the l samples before the current moment:

(8)

2.4. Presentation of Original Antibodies. In DAIS, antibodies and antigens are used to reflect the historical conditions and online conditions separately. In contrast to conventional AIS, in DAIS, the antibodies and antigens are represented by matrices of time-sampled data, instead of vectors of data, to reflect data changes in trend.21 In DAIS, antibodies are either generated from data directly or through the clone with mutation. The antibodies that are generated from data are called original antibodies. To obtain original antibodies, first the samples should be normalized to eliminate the amplitude differences among variables, as shown in eq 9:

X=

i=1

T l × n = [T (1); T (2); ...; T (l)]

t ∑i = 1 |φ(i)|

t

∑ [HF(i + 1 − s) − HN(k + 1 − s)]

2.5. Presentation of Antigens. During fault detection and diagnosis, the last l samples before the current sampling point compose a real-time data matrix:

(7)

Finally, the normalized difference η between R and T could be calculated as η(Ag, Ab) =

s

AbmN× n = [HN(1); HN(2); ...; HN(m)]

n c=1

1 s

In this paper, we assume a value of s = 5. The selection of s may affect the FDD performance of the antibody libraries, so further research on the selection of s is necessary. The original normal antibody is composed of the normal historical data:

where j(l) = j*. According to this sequence F*, a difference matrix φ can be calculated by φ (i ) =

(11)

where M1×n is a 1 × n modification item obtained by averaging s the difference of s sampling points before the first sampling points of T between T and HN:

(10)

where k is the sequence number of a normal startup sampling point that associate with the fault introduction moment according to the sequence matching the historical normal sample and fault sample, according to eqs 1−6. HF(1) is the

Ms1 × n = C

1 s

s

∑ [T(i + 1 − s) − HN(k + 1 − s)] i=1

(18)


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Industrial & Engineering Chemistry Research In this paper, we assume a value of s = 5. Research in the future will focus on the selection of s. 2.6. Antibody Library Construction. After the original antibodies are generated, they should be cloned with mutation to acquire enough antibodies to construct an antibody library. If there is only one original antibody X0 of one type, then X* indicates the antibody cloned from X0, while a indicates a random number from 0.5 and 2. The new antibody X* can be cloned with mutation by X * = aX 0

infectious pathogen or a disease process. The vaccines are, indeed, antigens that are presented to the HIS, and the antigen materials used for vaccination can be live-attenuated pathogens, killed or inactivated forms of pathogens, or purified or recombinant materials, such as proteins.35 Learning from the idea of vaccine transplant to the HIS, we may assume that historical samples from other chemical processes of the same type can be regarded as vaccines and used to help improve the response of the DAIS to the faults in a chemical process where no historical samples of the faults are available. In such a FDD framework, the historical samples from other chemical processes have similar effects on DAIS as the effect of vaccines on HIS. Based on this idea, we propose a new DAIS approach for FDD with vaccine transplant in this paper. In our approach, the difference matrices between fault historical samples and normal historical samples from other chemical processes are first calculated using the fault antibody generation described by eqs 9−13. These difference matrices are called vaccines in our approach. The vaccines contain the information on the deviation trend caused by the faults. They can be transplanted to the chemical process to be diagnosed with the help of already-established fault antibody libraries. Thus, the vaccines in our approach play a similar role as the vaccines does in medicine. The chemical processes that offer the vaccines are called the vaccine source processes. The processes to be diagnosed are called diagnosis objective processes. In conventional AIS, new antibodies are generated from original antibodies through a clone-with-mutation process. In our approach, vaccines are used to help generate new antibodies. If there exist some original antibodies, vaccines and original antibodies can be put together and cloned with mutation. If no original antibodies exist, only vaccines are to be cloned with mutation. The generation of new antibodies includes the following steps: (1) Choose the historical fault samples and historical normal samples from the vaccine source processes under similar operating conditions with the diagnosis object processes. Generate original fault antibodies in vaccine source processes using eqs 9−13. These original fault antibodies then are used as vaccines in the diagnosis objective process and are denoted as V. (2) Randomly select two fault vaccines V1 and V2. The cloned antibody (V*), then can be obtained by

(19)

If there are more than two original antibodies in one type of fault library, then two antibodies should be taken randomly from the library. Let X1 and X2 represent the two original antibodies; calculate the difference matrixes φ* between the two antibodies by using eq 8. Herein, in this paper, X* indicates an antibody cloned from X1 and X2 with mutation, a indicates a random number between 0.5 and 2, and b indicates a random number between −1 and 1. The new antibody X* can be cloned with mutation by X * = aX1 + bφ *

(20)

In eqs 19 and 20, the parameters a and b represent the magnitudes of mutation during the clone. They are tunable and we select the same values of them as Dai and Zhao’s work in 2011.22 The relationships between the values of these parameters and the performance of the cloned antibodies will be studied in the future. A threshold is necessary for each antibody library as criteria to determine whether an antigen is in the same status represented by the antibody library. If an antibody library has an antibody whose difference from the antigen is smaller than the antibody library threshold, then the antigen is recognized by the antibody library. That means that the process is in the status represented by the antibody library’s type. If the antibody library is the normal state antibody library, then the process is in the normal state. If the antibody library is a certain fault’s antibody library, then the process is in the fault’s state. To calculate the threshold, a matrix η is constructed by the difference between any two antibodies in the same type of library using the DTW algorithm. Let η(i,j) indicate the degree of difference between antibody i and antibody j calculated according to DTW, and let η(i,i) = ∞ to avoid considering the differences between an antibody and itself. Hence, the threshold of this library will be n

n

i=1

j=1

δ = max(min η(i , j))

V * = aV1 + b(V1 − V2)

(22)

where a is a random number between 0.5 and 2 and b is a random number between −1 and 1. The selection of these values are also based on the 2011 work of Dai and Zhao,22 similar to eq 20. Repeat Step (2) until the total number of antibodies reaches the predefined size of the antibody library and then the antibody library of a certain fault type is built. In this paper, the size of each antibody library is defined as 100. 3.2. Fault Diagnosis Algorithm. After the fault antibody libraries are constructed through vaccine transplant, the fault diagnosis can be conducted. The framework of our proposed approach is shown in Figure 1. It consists of four parts: (1) initialization, (2) fault detection, (3) fault diagnosis, and (4) selflearning. 3.2.1. Initialization. Obtain original normal antibodies of the diagnosis objective process according to eq 13. Build the normal antibody library through clone with mutation according to eqs 19 and 20. If there are historical fault samples in the diagnosis objective process, then generate original fault antibodies and build fault antibody libraries through clone with mutation.

(21)

3. THE PROPOSED FDD APPROACH 3.1. Vaccine Transplant. In an operating chemical process, normal samples are usually plentiful and easy to obtain. Having plenty of samples, the original normal antibody library can be easily built. However, the chance for faults to occur is rather small and fault samples are usually rare. Samples of some types of faults may even not yet exist. In such cases, antibody libraries of such faults cannot be built under the present framework of DAIS,23 and, therefore, the fault cannot be diagnosed either. In HIS, similar problems also exist. Although the HIS is usually effective to eliminate anomalies, sometimes we are forced to suffer from the effect of pathogens before a complete immune response is established. In medicine, vaccines are used to evoke an immune response that improves the system’s resistance to the effects of an D


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Figure 1. Framework of DAIS with vaccine transplant.

result, a new original fault antibody is then generated from data starting from the fault detection moment. The new original fault antibody then is stored into the fault antibody library of the fault type of the manual diagnosis result. Afterward, the fault antibody library is updated through a new round of clones with mutation.

Then generate normal vaccines and fault vaccines from the data from the vaccine source process and transplant them into DAIS to construct fault antibody libraries through clone and mutation, according to Steps (1)−(5) in Section 3.1. Afterward, calculate the threshold of each antibody libraries according to eq 21. 3.2.2. Fault Detection. Generate detective antigens with online data according to eq 14. Calculate the difference between the detective antigen and each antibody in the normal antibody, using the DTW algorithm, according to eqs 1−8, and find the minimum difference. In the following part of this paper, this minimum difference will be called “the difference from the normal antibody library”. If the difference from the normal antibody library is greater than the threshold of the normal antibody library, then a fault is detected. Otherwise, the new set of data is used to generate a new normal antibody that stored in the normal antibody library. 3.2.3. Fault Diagnosis. After a fault is detected, generate a diagnostic antigen according to eqs 15 and 16. Then calculate the difference between the antigen and each antibody in fault antibody libraries of each fault type, using the DTW algorithm, according to eqs 1−8. For each fault antibody library, find the minimum difference of the antigen and the antibodies in the library. In the following part of this paper, this minimum difference will be called the difference between the antigen and the fault antibody library. Compare the difference and the threshold of the corresponding fault antibody library. If there exists a fault antibody that has a smaller difference than the threshold of the corresponding fault antibody library, then the fault is recognized of the specific fault type of the corresponding fault antibody library. If none of the fault antibody libraries contain an antibody that has a smaller difference than the corresponding threshold, the fault is then diagnosed as a new fault. 3.2.4. Self-Learning. After the fault diagnosis of DAIS, a manual diagnosis should be conducted to double-check the diagnosis results by DAIS. According to the manual diagnosis

4. CASE 1: TRANSPLANT BETWEEN SIMULATED PROCESSES The effectiveness of the proposed method is illustrated first with Pensim v2.0. Pensim v2.0 is a penicillin fed-batch simulator developed by Birol, Ü ndey, and Cinar.36 Figure2 shows the

Figure 2. Flowsheet of the Pensim process.

flowsheet of the process simulated by Pensim v2.0. Two proportional integral differential (PID) controllers are used to control the fermenter temperature and pH, which are critical to ensure product quality. The model can simulate the time-varying values of process variables under various operating conditions. E


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Industrial & Engineering Chemistry Research The simulated data generated by the model can be used for multivariate statistical process monitoring and fault diagnosis. The model has four input variables (aeration rate, agitator power, substrate feed rate, and substrate feed temperature), six internal state variables (culture volume, generated heat, concentrations of carbon dioxide, dissolved oxygen, biomass, penicillin, and substrate). Fermenter temperature and pH are the controlled variables while acid/base flow rates and heating/ cooling water flow rates are the manipulated variables. Considering the measurability of the variables in actual scenarios, seven variables were selected as the monitored variables in this case: aeration rate, agitator power, concentration of dissolved oxygen, concentration of carbon dioxide, culture volume, fermenter temperature, and fermenter pH. In this case study, the duration of each batch was set to be 400 h. All the batches were simulated with an integration step size of 0.02 h and a sampling interval of 0.1 h. To realize the process of vaccine transplant, two plants with different characteristics were simulated. Plant A, which is the vaccine source, is smaller than Plant B, which is the diagnostic object. Small variations were added to the process inputs and initial conditions to generate samples with process variations mimicking a realistic condition. The setting and variations of the process initial conditions and set points of the controlled variables are listed in Table 1.

Table 2. Setting of Test Fault Batches from Plant B

variable Initial conditions substrate concentration (g/L) dissolved oxygen concentration (mmol/L) biomass concentration (g/L) penicillin concentration (g/L) culture volume (L) carbon dioxide concentration (mmol/L) pH temperature (K) set points aeration rate set point (L/h) agitator power set point (W) substrate feed rate set point (L/h) substrate feed temperature set point (K) pH set point temperature set point (K)

mean value

max. variability

Plant B mean value

±0.5

20.0

±0.5

1.16

±0.01

1.60

0

0.10 0

0 0

0.20 0

±0.02 0

100 0.50

0 ±0.01

200 0.40

±2 ±0.02

5.0 298

0 0

5.0 298

±0.1 ±1

8.6 30.0 0.042

0 0 0

10.0 50.0 0.084

0 0 ±0.01

296

0

296

±1

5.0 298

0 0

5.0 298

0 0

magnitude (%)

occurrence moment (h)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

aeration rate step decreasing aeration rate step decreasing aeration rate step decreasing aeration rate step decreasing aeration rate step decreasing agitator power step decreasing agitator power step decreasing agitator power step decreasing agitator power step decreasing agitator power step decreasing substrate feed rate step decreasing substrate feed rate step decreasing substrate feed rate step decreasing substrate feed rate step decreasing substrate feed rate step decreasing

30 20 40 45 37 30 20 35 40 31 39 50 35 40 33

160 68 98 115 130 180 130 73 163 130 105 130 73 158 142

Table 3. Threshold of Antibody Libraries Constructed with Samples from Plant A

max. variability

15.0

fault type

In this case study, the length of each fault antibody was taken to be 20 and the length of each antigen was taken as 10. In the system initialization step, for each type of fault, 100 antibodies are generated using vaccines from Plant A to construct the fault antibody library. One hundred (100) normal antibodies are generated from 2 normal samples of Plant B to construct the normal antibody library. The threshold of each library then was calculated through eq 21. The thresholds of the antibody libraries are listed in Table 3.

Table 1. Initial Conditions and Set Points for Pensim Simulation Plant A

batch

antibody library name

description

threshold

normal fault 1 fault 2 fault 3

normal aeration rate step decreasing agitator power step decreasing substrate feed rate step decreasing

0.013 0.0114 0.0159 0.0012

After the construction of all the antibody libraries was completed, fault detection and diagnosis could be conducted, following the procedures in Section 3.2. During the fault detection, detective antigens were generated from the test sample at each sampling point, according to eq 15, and their differences from the normal antibody library were calculated. When the differences got larger than the threshold of the normal antibody library, faults were detected. After the faults were detected, diagnostic antigens were generated, according to eqs 16−18, and their differences from all three fault antibody libraries were calculated. The fault detected moment, as well as the diagnosed fault types, of all 15 test samples are listed in Table 4. To highlight whether the differences between the diagnostic antigens and the fault antibody libraries are larger or smaller than the antibody thresholds, they are shown in the form of quotients of the difference values divided by the antibody thresholds. Therefore, if a quotient is smaller than 1, the test sample is diagnosed to have the fault of the type of the corresponding antibody library. It can be concluded that all 15 of the fault batches from Plant B can be correctly diagnosed. That is to say, although no historical fault samples are available from Plant B, the fault antibody libraries constructed with samples from Plant A are able to diagnose faults with various fault magnitudes and occurrence

In Plant A, two normal batches and two fault batches of each of the three fault types were simulated to generate the original normal and fault antibodies and then to construct the antibody library and initialize the DAIS, as described in Section 2. Afterward, one normal batch and five test fault batches of each of the fault types are simulated in Plant B to generate antigens and diagnosed using the antibody libraries generated from Plant A. Table 2 shows the details of the test fault batches from Plant B. F


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Industrial & Engineering Chemistry Research Table 4. Diagnosis Results of Case 1 Difference Divided by Threshold batch

introduced fault type

fault introduced moment (h)

fault detected moment (h)

fault 1

fault 2

fault 3

diagnosed fault type

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15


105.0 140.0 147.0 200.0 150.0 140.0 120.0 150.0 130.0 140.0 140.0 160.0 120.0 158.0 146.0

105.2 140.2 147.3 200.3 150.3 140.3 120.2 150.3 130.3 140.3 141.1 161.0 121.0 160.5 147.1

0.18 0.33 0.13 0.18 0.18 29.42 37.48 33.41 37.82 35.65 13.18 13.18 13.18 13.18 13.19

25.23 27.66 35.60 20.97 32.92 0.21 0.31 0.42 0.25 0.40 16.79 16.80 16.80 16.02 16.80

249.67 291.42 416.17 166.67 375.33 250.00 333.42 291.75 336.92 314.75 0.17 0.25 0.17 0.67 0.33


Figure 3. Test fault batch 14 and normal batch in Plant B.

ηt = min(η0), which presented the difference between the antigen and the normal antibodies, was obtained by finding the minimum η0(i). Then, ηt was compared with the threshold of the normal antibody library to detect faults. As Figure 5 shows, before moment 158 h, the difference was smaller than the threshold so no faults were detected. At a moment of 158 h, the fault was introduced but the deviation from the normal state was not significant, so the difference was still smaller than the threshold. After 25 sampling points, the difference became larger than the threshold, so the fault was detected and the fault diagnosis started. After the fault was detected, the diagnostic antigen was generated using eqs 16−18. Then, ηk(i), which represents the difference between the antigen and antibody i from fault antibody library k was calculated using eqs 3−8. Let ηk = min(ηk(i)), which presented the difference of the antigen and the fault antibody library k and compared it with δk, the threshold. As Table 5 shows, η1 and η2 are always larger than δ1 and δ2, while η3 became smaller than δ3. Therefore, the fault type was diagnosed as substrate feed rate decreasing.

moments in Plant B, which further illustrates the effectiveness of the proposed method of vaccine transplant. Take the diagnosis of fault batch 14 in Plant B as an example. The test batch introduced a fault of 40% substrate feed rate step decreasing at a moment of 158 h. Figure 3 shows the normalized variables selected for fault diagnosis of test batch 14 and a normal batch in Plant B. Figure 4 shows the same set of variables of a

Figure 4. Historical batches in Plant A (the fault type is “substrate feed rate decreasing”).

5. CASE 2: TRANSPLANT BETWEEN LABORATORY-SCALE DISTILLATION PLANTS OF DIFFERENT COLUMN TYPES The laboratory-scale distillation plant used for the case study is designed especially for fault diagnosis study. Several types of faults can be introduced into the plant. The laboratory-scale

normal batch and two fault batches with the same type of fault and different fault introduction moments in Plant A. At moment t, 10 samples before t were used to generate the detective antigen. η0(i), which indicated the antigen and the normal antibody i, was calculated according to eqs 3−8. Then, G


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Figure 5. Fault detection of fault batch 14 in Plant B.

Each of the columns has a height of 2.2 m and a width of 75 mm. The plate column has 15 trays and the feed enters at tray 12 from top of the column. The feed height to the packed column is the same as the feed to the plate column. A distributed control system (DCS) is used to control the plant and collect data that are stored in a real-time database ASPEN Infoplus.21. In each of the columns, three PID controllers are used to control condenser’s level, reboiler’s level, and cooling water rate, respectively. Three metering pumps are used to control feed, reflux, and bottom product flow rate. In each of the columns, there are 21 measured variables monitored by the DCS system, including 13 temperature variables, 2 pressure variables, 4 flow rate variables, and 2 liquid level variables. Also, 2 manipulated variables representing the V-6 position and the V-18 position are stored in the DCS system and transmitted to the real-time database. The sampling interval of the DCS system and the real-time database is set to be 1 s. In each column, 11 variables are used for fault detection and diagnosis, including the pressures at the top and bottom of the column (P101 and P102, or P111 and P112), 8 column temperature measures (T101−T108, or T111−T118), and T203, the inlet temperature measure of the reflux tank. Although the two columns share the same condenser and reflux tank, their column structures and reboilers are different. The process flow diagram (PFD) of the distillation plants shown in Figure 6, where all the measured variables can be found. The normal start-up time of each of the distillation columns is ∼30 min. Before the start-up operation, except for the cooling water valves V17 and V19 and the vent valve V15, all other valves are in the closed state. Steps of the start-up operation of the plate column are shown in Table 6. Start-up steps of the packed column are similar, except that V-2, V-3, V-4, T102, and LIC101 are replaced by V-25, V-23, V-26, T112, and LIC111, respectively.

distillation plant includes a plate column (T101) and a packed column (T102) in parallel, so each column can serve as a vaccine source to offer vaccines to conduct fault diagnosis in the other. Table 5. Difference between Antigen of Batch 14 and the Fault Antibody Libraries 1 2 3

fault antibody library

difference

threshold

aeration rate step decreasing agitator power step decreasing substrate feed rate step decreasing

0.1502 0.2547 0.0008

0.0114 0.0159 0.0012

diagnosed fault type: substrate feed rate step decreasing

Figure 6. Process flow diagram of the distillation experiment plant.

Table 6. Start-Up Procedure of the Plate Column step

procedure

1

open valves V2, V3, V9, V10, and V11; add an ethanol−water solution with a volume fraction of 30% into the column bottom using a full-speed feed pump P201 under the room temperature and atmospheric pressure when the column bottom liquid level exceeds 27.5 cm, turn off the full-speed feed pump P201 and valves V10 and V11; heat the column bottom with a load of 100%; adjust the opening of V18 to make the cooling water flow rate ∼150 L/h when the first column plate temperature T102 reaches 70 °C, reduce the heating load of the column bottom to 60%; open valves V12 and V13; set a reflux accumulator liquid level controller LIC102 to automatic and set the SV value of the reflux accumulator liquid level controller LIC102 to 4 cm when the reflux accumulator liquid level is substantially stable, open valves V4, V5, V6, V7, and V8; start the feed metering pump P101; set its feeding flow rate to 10 L/h; set the column bottom liquid level controller LIC101 to automatic; and set its SV value to 25 cm when the column bottom liquid level is substantially stable, open valve V14, start the product metering pump, start the reflux ratio controller, and set the reflux ratio to 2

2 3 4 5

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“cooling water shutdown”. The fault “reboiler shutdown” was introduced during the startup while the fault “backup heater open by mistake” and “cooling water shutdown” were introduced during the steady-state operation after a normal startup had been completed. The packed column was operated for the purpose of generating vaccines. For each type of fault, two sets of fault samples were generated and collected by introducing the fault to the packed column with different magnitudes and different introduction moments, so there were two vaccines of each fault type. The plate column then was operated to generate original antibodies. Original normal antibodies were generated from the normal data of the plate column. After the original antibodies and vaccines were generated, then antibody libraries could be constructed for online fault detection and diagnosis. A normal antibody library was constructed with mutation of the original normal antibodies. A fault antibody library of each fault type was constructed with the normal and fault vaccines, according to Section 3. Thresholds of all the antibody libraries are calculated with eq 21. The thresholds of the normal and fault antibody libraries are shown in Table 8. Test fault samples from the plate column then were used to test the effectiveness of the DAIS with vaccine transplant. The test samples were first used to generate detective antigens to detect their faults, and after faults were detected, diagnostic antigens were generated to diagnose the fault types, which is similar to the FDD in the case study on Pensim. The results of fault diagnosis on other fault samples are listed in Table 9. Take the detection and diagnosis of Sample 1 of fault “reboiler shutdown” for example.

After the start-up operation is completed, the steady-state distillation lasts for ∼2 h. The main operating parameters and control targets of controllers during the steady-state operation are shown in Table 7. In this case study, we used the packed column as the vaccine source and tried to diagnose faults in the plate column. In this paper, a total of three types of faults were studied, including “reboiler shutdown”, “backup heater open by mistake”, and Table 7. Parameter Settings under Normal Steady-State Operating Conditions parameter Operating parameters column bottom heating power operating pressure feed ethanol concentration feeding flow rate condensed water flow rate reflux ratio Control targets column bottom liquid level reflux accumulator liquid level

variable symbol

value

W P101/P111 C F101 F104 R

15.0 ± 0.5 kW 1 atm 30% ± 1% (v/v) 10.0 L/h 150 ± 10 L/h 2

L101/L111 L102

30 cm 4 cm

Table 8. Thresholds of the Fault Antibody Libraries antibody library name

description

threshold

normal fault 1 fault 2 fault 3

normal state reboiler shutdown backup heater open cooling water shutdown

0.22 0.28 0.19 0.22

Table 9. Fault Diagnosis Results of Case 2 Difference Divided by Threshold sample

fault introduced moment (s)

fault detected moment (s)

fault 1

fault 2

fault 3

1 2

reboiler shutdown reboiler shutdown

fault type

1276 990

1303 1005

0.61 0.48

3.25 4.56

2.62 1.77



3 4

backup heater open backup heater open

1369 1620

1380 1628

1.52 1.13

0.81 0.63

1.31 1.15


5 6

cooling water shutdown cooling water shutdown

1958 1932

2008 1968

1.26 1.16

1.63 1.69

0.31 0.15


Figure 7. Fault detection of “reboiler shutdown”. I


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pressure (the blue solid curve) to decrease. The red curve, which represented the difference between the antigen and the normal antibody library, ascended because of the fault but was still below the threshold of normal antibody library (the purple solid line). At the 1303th second, the difference from the normal antibody library became larger than the threshold, so a fault was detected and the online data from the 1272th second to the 1303th second were used to generate a diagnostic antigen whose length was 30 sampling points. After the fault diagnosis was conducted, the diagnostic antigen was compared with the antibodies in each of the fault antibody libraries. Table10 shows the differences between the antigen and each antibody library. It can be found that only the antibody library of “Reboiler shutdown” has a difference from the antigen that is below the threshold. Thus, the faults can be correctly diagnosed.

Table 10. Diagnosis Results of Sample 1 in Case 2 fault antibody library

difference from fault antibody library

threshold

reboiler shutdown backup heater open cooling water shutdown

0.19 0.52 0.34

0.28 0.19 0.22

diagnosed fault type: reboiler shutdown

Table 11. Variables in Two Columns variable description

column A

column B

column top temperature column bottom temperature number of tray temperatures reflux tank inlet temperature column top pressure column bottom pressure

√ √ 6 √ √ √

√ √ 10 √ √

6. CASE 3: TRANSPLANT BETWEEN LABORATORY-SCALE DISTILLATION PLANTS OF DIFFERENT COLUMN SIZES Another case study was performed between two laboratory-scale distillation columns, which are plate columns of different sizes. One of the columns was the plate column that was described in Case 2, and the other one was a larger column, with a height of 4 m and a width of 100 mm. It has 10 trays and the feed enters at tray 7 from the top of the column. Later in this section, the smaller column will be called column A and the larger one will be called column B. In column B, distributed control systems (DCSs) are also used to control the processes and collect data that are stored in realtime databases. PID controllers are also used to control the condenser level, the reboiler level, and the cooling water rate. Since the sensor deployments of the two columns are different, the measured variables of them are different, as Table 11 shows. Because of the difference of sensor deployments, the variables of the two columns also had to be associated. In this case, the association was done manually. The variable association between the two columns is shown in Table 12. The main difference of sensor deployments was in the tray temperatures. We retained the six tray temperatures in Column A and selected six tray temperatures in Column B in the same order, from top to bottom, to associate them separately. The three types of faults in Case 2“reboiler power shutdown”, “backup heater open”, and “cooling water shutdown”were introduced into Column B to generate fault samples. Two samples of each fault type were collected. These fault samples then were used to generate vaccines to build fault antibody libraries according to eqs 10−12. Afterward fault samples in Column A were generated and diagnosed with these

Table 12. Variable Association in Vaccine Transplant of Case 3 variable

column A

column B

1 2 3 4 5 6 7 8 9 10

column top temperature column bottom temperature reflux tank inlet temperature column bottom pressure tray 1 temperature tray 2 temperature tray 3 temperature tray 4 temperature tray 5 temperature tray 6 temperature

column top temperature column bottom temperature reflux tank inlet temperature column bottom pressure tray 1 temperature tray 3 temperature tray 5 temperature tray 6 temperature tray 8 temperature tray 10 temperature

Table 13. Thresholds of the Fault Antibody Libraries antibody library name

description

threshold

fault 1 fault 2 fault 3


0.17 0.18 0.12

First, fault detection was conducted with the online data. In Figure 7, the blue and green curves show the data of 4 variables out of the 11 variables for fault detection and diagnosis from the beginning of the startup to ∼3 min after the fault was introduced. The red curve shows the difference between the antigen and the normal antibody library. The antigen was generated from the last 30 samples before the current sampling point, so it and the difference continually varied. The fault was introduced at the 1276th second and immediately caused the column bottom Table 14. Fault Diagnosis Results of Case 3

Difference Divided by Threshold sample

fault introduced moment (s)

fault detected moment (s)

fault 1

fault 2

fault 3

1 2


fault type

1276 990

1303 1005

0.41 0.59

1.75 2.06

3.75 4.17


3 4


1369 1620

1380 1628

2.88 2.12

0.25 0.31

2.67 2.08


5 6


1958 1932

2008 1968

1.24 1.12

2.33 1.50

0.42 0.17


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determine whether the transplant is practical. Second, there are several tunable parameters including s in eqs 12 and 18, a and b in eqs 19, 20, and 22, the sizes of antibody libraries, and the lengths of antibodies and antigens. The selection of their values, and the relationships between their values and the FDD performance of the proposed method, as well as the original DAIS, are worth studying.

antibody libraries. According to the calculation results of eq 21, the thresholds of fault antibody libraries are listed in Table 13. The test samples from Column A then were diagnosed with these fault antibody libraries. The fault detection is the same as the case study of vaccine transplant from the packed column to the plated column in Section 5, because, in these two cases, the test samples and historical normal samples are both from the laboratory-scale plated column. As for the fault diagnosis, the differences between the diagnostic antigens and the three fault antibody libraries, as well as the diagnosed fault types, are listed in Table 14. Take the detection and diagnosis of Sample 1 of fault “reboiler shutdown” for example again. The fault detection was the same as it was in Section 4, because of the same test samples and historical normal samples. In the fault diagnosis, the differences between the diagnostic antigen and the antibodies in each of the fault antibody libraries are shown in Table 15. It can be found that

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Corresponding Author

*Tel.: +86 10 62783109. Fax: +86 10 62770304. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge support from the National High-Tech R&D Program of China (863 Program) (No. 2013AA040702) and the National Natural Science Foundation of China (No. 61433001).

Table 15. Diagnosis Results of Sample 1 in Case 3 fault antibody library

difference from fault antibody libraries

threshold


0.07 0.28 0.45

0.17 0.18 0.12

AUTHOR INFORMATION

■

diagnosed fault type: reboiler shutdown

only the antibody library of “reboiler shutdown” has a difference from the antigen that is below the threshold. So the faults can be correctly diagnosed.

7. CONCLUSION Apart from the reduction of cost and waste, the prevention of faults and accidents is also important to ensure the sustainability of manufacturing. Therefore, fault detection and diagnosis (FDD) also plays an important role in sustainable manufacturing. Many FDD methods have been developed over the past decades. Among them, artificial immune system (AIS) shows strong selfadaptive capability in fault diagnosis. However, the application of FDD methods is still limited. One of the reasons is the scarcity of fault samples. To address this problem, we have proposed a new FDD approach simulating the vaccine transplant process in medicine. Normal antibodies for fault detection are still generated from the normal historical samples as they are done in conventional AIS. What is different is that fault antibodies are generated from the so-called “vaccines”. Thus, the faults can be diagnosed with the fault trend information from processes of the same type in cases where historical fault samples are not available from the monitored process. Case studies have been performed on the Pensim simulated process and distillation experiment plants of different column types and of different sizes. Diagnosis results show that the antibodies generated from the vaccines from processes of the same type can successfully identify the faults with various faultintroduced moments and fault magnitudes, although those faults never occurred before in the diagnosed process. The results illustrate the effectiveness of the vaccine transplant method. There are still some issues that must be solved in the future work. First, the measurement of the “transplantability” should be studied. In other words, the analysis of the similarity of processes from which the vaccines are transplanted is necessary to

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ACRONYMS AIS = artificial immune system ANN = artificial neural network DAIS = dynamic artificial immune system DCS = distributed control system DLA = dynamic locus analysis DTW = dynamic time warping HIS = human immune system ICA = independent component analysis PCA = principal component analysis PFD = process flow diagram PLS = partial least-squares REFERENCES

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Fault Diagnosis of Chemical Processes Using Artificial Immune

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